Average square speed in Maxwell—Boltzmann statistics

For an ideal gas, the average square of speed is directly proportional to its temperature and inversely proportional to the mass of the gas.

Notation:

1. \(k_\text{B}\) (k_B) is boltzmann_constant.

Conditions:

1. The gas is in thermal equilibrium with the environment.

2. The gas particles are distributed according to Maxwell—Boltzmann statistics.

Links:

1. Wikipedia.

average_square_speed

Average square of the speed of gas molecules.

Symbol:

avg(v^2)

Latex:

\(\langle v^2 \rangle\)

equilibrium_temperature

Equilibrium temperature of the gas.

Symbol:

T

Latex:

\(T\)

Dimension:

temperature

molecular_mass

mass of a gas molecule.

Symbol:

m

Latex:

\(m\)

Dimension:

mass

law

avg(v^2) = 3 * k_B * T / m

Latex:

\[\langle v^2 \rangle = \frac{3 k_\text{B} T}{m}\]